Fast and accurate MAS–DNP simulations of large spin ensembles

A deeper understanding of parameters affecting Magic Angle Spinning Dynamic Nuclear Polarization (MAS–DNP), an emerging nuclear magnetic resonance hyperpolarization method, is crucial for the development of new polarizing agents and the successful implementation of the technique at higher magnetic fields (>10 T). Such progress is currently impeded by computational limitation which prevents the simulation of large spin ensembles (electron as well as nuclear spins) and to accurately describe the interplay between all the multiple key parameters at play. In this work, we present an alternative approach to existing cross-effect and solid-effect MAS–DNP codes that yields fast and accurate simulations. More specifically we describe the model, the associated Liouville-based formalism (Bloch-type derivation and/or Landau–Zener approximations) and the linear time algorithm that allows computing MAS–DNP mechanisms with unprecedented time savings. As a result, one can easily scan through multiple parameters and disentangle their mutual influences. In addition, the simulation code is able to handle multiple electrons and protons, which allows probing the effect of (hyper)polarizing agents concentration, as well as fully revealing the interplay between the polarizing agent structure and the hyperfine couplings, nuclear dipolar couplings, nuclear relaxation times, both in terms of depolarization effect, but also of polarization gain and buildup times.